Decorrelation-Based Feature Discovery: DARWIN-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

1.2 The Data

DARWIN <- read.csv("~/GitHub/FCA/Data/DARWIN/DARWIN.csv")
rownames(DARWIN) <- DARWIN$ID
DARWIN$ID <- NULL
DARWIN$class <- 1*(DARWIN$class=="P")
print(table(DARWIN$class))
#> 
#>  0  1 
#> 85 89

DARWIN[,1:ncol(DARWIN)] <- sapply(DARWIN,as.numeric)

signedlog <- function(x) { return (sign(x)*log(abs(1.0e12*x)+1.0))}
whof <- !(colnames(DARWIN) %in% c("class"));
DARWIN[,whof] <- signedlog(DARWIN[,whof])

1.2.0.1 Standarize the names for the reporting

studyName <- "DARWIN"
dataframe <- DARWIN
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
174	450

pander::pander(table(dataframe[,outcome]))

0	1
85	89

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9994118

1.5 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 450 , Uni p: 0.006594985 , Uncorrelated Base: 139 , Outcome-Driven Size: 0 , Base Size: 139 
#> 
#> 
 1 <R=0.999,thr=0.900,N=  261>, Top: 91( 1 )[ 1 : 91 Fa= 90 : 0.900 ]( 90 , 166 , 0 ),<|>Tot Used: 256 , Added: 166 , Zero Std: 0 , Max Cor: 0.992
#> 
 2 <R=0.992,thr=0.900,N=  261>, Top: 16( 1 )[ 1 : 16 Fa= 105 : 0.900 ]( 16 , 26 , 90 ),<|>Tot Used: 258 , Added: 26 , Zero Std: 0 , Max Cor: 0.959
#> 
 3 <R=0.959,thr=0.900,N=  261>, Top: 2( 1 )[ 1 : 2 Fa= 107 : 0.900 ]( 2 , 2 , 105 ),<|>Tot Used: 258 , Added: 2 , Zero Std: 0 , Max Cor: 0.899
#> 
 4 <R=0.899,thr=0.800,N=  136>, Top: 65( 2 )[ 1 : 65 Fa= 144 : 0.800 ]( 59 , 67 , 107 ),<|>Tot Used: 339 , Added: 67 , Zero Std: 0 , Max Cor: 0.993
#> 
 5 <R=0.993,thr=0.900,N=    4>, Top: 2( 1 )[ 1 : 2 Fa= 145 : 0.900 ]( 2 , 2 , 144 ),<|>Tot Used: 339 , Added: 2 , Zero Std: 0 , Max Cor: 0.894
#> 
 6 <R=0.894,thr=0.800,N=   25>, Top: 12( 1 )[ 1 : 12 Fa= 147 : 0.800 ]( 12 , 13 , 145 ),<|>Tot Used: 343 , Added: 13 , Zero Std: 0 , Max Cor: 0.842
#> 
 7 <R=0.842,thr=0.800,N=   25>, Top: 1( 1 )[ 1 : 1 Fa= 147 : 0.800 ]( 1 , 1 , 147 ),<|>Tot Used: 343 , Added: 1 , Zero Std: 0 , Max Cor: 0.797
#> 
 8 <R=0.797,thr=0.800,N=   25>
#> 
 [ 8 ], 0.7971926 Decor Dimension: 343 Nused: 343 . Cor to Base: 213 , ABase: 88 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

692

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

123

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

4.57

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

4.65

1.5.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPSTM <- attr(DEdataframe,"UPSTM")
  
  gplots::heatmap.2(1.0*(abs(UPSTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.7971926

1.8 U-MAP Visualization of features

1.8.1 The UMAP based on LASSO on Raw Data

if (nrow(dataframe) < 1000)
{
  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}

1.8.2 The decorralted UMAP

if (nrow(dataframe) < 1000)
{

  datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}

1.9 Univariate Analysis

1.9.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : mean_jerk_in_air6 200 : disp_index12 300 : mean_speed_in_air17 400 : gmrt_on_paper23

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_mean_jerk_in_air6 200 : La_disp_index12 300 : mean_speed_in_air17 400 : gmrt_on_paper23

1.9.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
total_time23	37.2	0.503	36.7	0.484	1.03e-05	0.863
total_time15	38.1	0.875	37.1	0.421	5.44e-01	0.844
air_time23	36.6	0.626	35.9	0.656	6.92e-03	0.844
air_time15	37.7	1.094	36.6	0.615	5.06e-01	0.829
total_time17	38.5	0.681	37.8	0.614	4.00e-03	0.824
paper_time23	36.4	0.439	36.0	0.231	6.72e-01	0.814
air_time17	37.9	0.914	37.0	0.795	3.52e-02	0.806
paper_time17	37.6	0.395	37.2	0.439	1.28e-03	0.796
total_time6	37.1	0.777	36.4	0.447	7.16e-01	0.790
air_time16	36.4	1.131	35.2	0.867	9.38e-01	0.787

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
air_time23	36.612	0.626	35.858	0.656	6.92e-03	0.844
air_time15	37.720	1.094	36.607	0.615	5.06e-01	0.829
air_time17	37.912	0.914	37.000	0.795	3.52e-02	0.806
air_time16	36.357	1.131	35.240	0.867	9.38e-01	0.787
disp_index23	16.116	0.194	15.926	0.166	3.43e-01	0.787
air_time6	36.694	0.899	35.811	0.665	7.39e-01	0.784
air_time7	36.742	0.758	36.090	0.938	5.42e-04	0.779
gmrt_in_air7	32.948	0.405	33.382	0.396	9.99e-01	0.775
air_time2	36.256	1.176	35.088	1.002	2.05e-01	0.773
mean_speed_in_air17	29.116	0.493	29.551	0.389	4.85e-01	0.766
La_gmrt_on_paper18	2.043	0.759	2.509	0.780	1.74e-02	0.728
La_mean_speed_on_paper2	2.121	0.820	2.805	0.864	7.19e-01	0.724
La_mean_speed_on_paper13	-5.051	0.068	-5.017	0.107	2.18e-05	0.718
La_pressure_mean3	0.286	0.506	0.652	0.408	2.87e-01	0.715
La_max_x_extension14	0.825	0.702	1.355	0.687	1.20e-01	0.712

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.25	221	0.491

theCharformulas <- attr(dc,"LatentCharFormulas")


finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores
total_time23	NA	37.231	0.503	36.666	0.484	1.03e-05	0.863	0.863	NA
total_time15	NA	38.092	0.875	37.146	0.421	5.44e-01	0.844	0.844	NA
air_time23	NA	36.612	0.626	35.858	0.656	6.92e-03	0.844	0.844	1
air_time231	NA	36.612	0.626	35.858	0.656	6.92e-03	0.844	NA	NA
air_time15	NA	37.720	1.094	36.607	0.615	5.06e-01	0.829	0.829	1
air_time151	NA	37.720	1.094	36.607	0.615	5.06e-01	0.829	NA	NA
total_time17	NA	38.526	0.681	37.848	0.614	4.00e-03	0.824	0.824	NA
paper_time23	NA	36.401	0.439	36.001	0.231	6.72e-01	0.814	0.814	NA
air_time17	NA	37.912	0.914	37.000	0.795	3.52e-02	0.806	0.806	1
air_time171	NA	37.912	0.914	37.000	0.795	3.52e-02	0.806	NA	NA
paper_time17	NA	37.604	0.395	37.205	0.439	1.28e-03	0.796	0.796	NA
total_time6	NA	37.100	0.777	36.368	0.447	7.16e-01	0.790	0.790	NA
air_time16	NA	36.357	1.131	35.240	0.867	9.38e-01	0.787	0.787	1
air_time161	NA	36.357	1.131	35.240	0.867	9.38e-01	0.787	NA	NA
disp_index23	NA	16.116	0.194	15.926	0.166	3.43e-01	0.787	0.787	1
air_time6	NA	36.694	0.899	35.811	0.665	7.39e-01	0.784	0.784	1
air_time7	NA	36.742	0.758	36.090	0.938	5.42e-04	0.779	0.779	1
gmrt_in_air7	NA	32.948	0.405	33.382	0.396	9.99e-01	0.775	0.775	1
air_time2	NA	36.256	1.176	35.088	1.002	2.05e-01	0.773	0.773	1
mean_speed_in_air17	NA	29.116	0.493	29.551	0.389	4.85e-01	0.766	0.766	4
La_gmrt_on_paper18	- (1.991)disp_index18 + gmrt_on_paper18	2.043	0.759	2.509	0.780	1.74e-02	0.728	0.647	4
La_mean_speed_on_paper2	- (1.577)disp_index2 + mean_speed_on_paper2	2.121	0.820	2.805	0.864	7.19e-01	0.724	0.720	3
La_mean_speed_on_paper13	- (1.035)gmrt_on_paper13 + mean_speed_on_paper13	-5.051	0.068	-5.017	0.107	2.18e-05	0.718	0.626	-1
La_pressure_mean3	- (0.265)disp_index3 - (1.199)mean_acc_on_paper3 + pressure_mean3	0.286	0.506	0.652	0.408	2.87e-01	0.715	0.341	3
La_max_x_extension14	- (2.106)disp_index14 + max_x_extension14	0.825	0.702	1.355	0.687	1.20e-01	0.712	0.634	-1

1.10 Comparing IDeA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	78	7
1	7	82

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.920	0.869	0.955
3	se	0.921	0.845	0.968
4	sp	0.918	0.838	0.966
6	diag.or	130.531	43.775	389.223

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	80	5
1	10	79

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.914	0.862	0.951
3	se	0.888	0.803	0.945
4	sp	0.941	0.868	0.981
6	diag.or	126.400	41.340	386.478

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	65	20
1	2	87

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.874	0.815	0.919
3	se	0.978	0.921	0.997
4	sp	0.765	0.660	0.850
6	diag.or	141.375	31.905	626.443

par(op)

1.11.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	82	3
1	10	79

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.925	0.876	0.960
3	se	0.888	0.803	0.945
4	sp	0.965	0.900	0.993
6	diag.or	215.933	57.299	813.755

  par(op)